Model predictive control suitable for closed-loop re-identification

The main problem of a closed-loop re-identification procedure is that, in general, the dynamic control and identification objectives are conflicting. In fact, to perform a suitable identification a persistent excitation of the system is needed, while the control objective is to stabilize the system to a given equilibrium point. In this work, a generalization of the concept of stability, from punctual stability to (invariant) set stability, is studied to avoid the conflict between these objectives. Furthermore, a persistent excitation scheme is proposed to properly perform a closed-loop re-identification. Simulation results show the propose controller formulation properties.